Neural Symbolic Regression of Complex Network Dynamics
Haiquan Qiu, Shuzhi Liu, Quanming Yao
TL;DR
This paper introduces PI-NDSR, a neural-symbolic approach that automatically learns symbolic representations of complex network dynamics from noisy data, combining neural interpolation and genetic programming.
Contribution
It presents a novel method integrating neural networks and genetic programming to effectively derive symbolic network dynamics from noisy observations.
Findings
Outperforms existing methods in recovery probability
Achieves lower error rates on synthetic datasets
Successfully models real disease spreading data
Abstract
Complex networks describe important structures in nature and society, composed of nodes and the edges that connect them. The evolution of these networks is typically described by dynamics, which are labor-intensive and require expert knowledge to derive. However, because the complex network involves noisy observations from multiple trajectories of nodes, existing symbolic regression methods are either not applicable or ineffective on its dynamics. In this paper, we propose Physically Inspired Neural Dynamics Symbolic Regression (PI-NDSR), a method based on neural networks and genetic programming to automatically learn the symbolic expression of dynamics. Our method consists of two key components: a Physically Inspired Neural Dynamics (PIND) to augment and denoise trajectories through observed trajectory interpolation; and a coordinated genetic search algorithm to derive symbolic…
Peer Reviews
Decision·Submitted to ICLR 2025
The results on these datasets show the good performance of the method, with some proof of robustness too. This applies to the real world dataset too, where the extracted dynamics of this method don't have "un-physical" properties. The ablation studies show that both parts of the algorithm are necessary for the best performance
It is not clear if this method could scale to real world datasets that have more complex dynamics, since there is only a single real-world dataset.
**Novel Approach** The use of genetic programming for symbolic regression of complex network dynamics is innovative as it constrains the symbolic search space, thereby helping to mitigate overfitting. Moreover, this approach does not rely on a predefined function library. **Improved Performance** PI-NDSR outperforms existing methods in terms of recovery probability and error, as demonstrated by experiments on various datasets. **Robustness** By incorporating neural ODEs, the method demonstrate
**Limited Novelty in Applying NeuralODE for Interpolation** The use of neural networks to model differential equations for interpolation is not particularly novel and has been addressed in prior research. With respect to the interpolation method, the paper does not introduce any methodological innovations.
**Addresses a Novel Challenge of Data Sparsity and Noise in Symbolic Regression**: The PI-NDSR method effectively tackles the issue of sparse and noisy data in symbolic regression by introducing a neural dynamics module that performs interpolation and denoising, making it suitable for complex network data with inconsistent quality. **Improves Genetic Algorithm for Symbolic Regression**: By incorporating a coordinated genetic search that uses neural dynamics as a reference, PI-NDSR refines the
**Lack of Novelty in Using Neural Networks for Differential Equation Interpolation**: Modeling differential equations with neural networks to achieve interpolation is not particularly novel and has been explored in previous works. This may limit the perceived innovation in the proposed approach’s foundational methodology. **Potential Oversmoothing from Interpolation without Fully Addressing Data Sparsity**: While the method employs interpolation to handle data sparsity, it does not adequately a
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Taxonomy
TopicsNeural Networks and Applications